This has been puzzling me for quite some time.
Suppose I have som data, that I have justefied should be described using a GLM model with a poisson as response.
As for choice of link function, You would normally go for the $log_e $function, and I understand that to be the case. Since we ofte observe, when working with count data. That the effekt of an observation is proportional to the side of size of the observation (ie. The predicter should be multiplicatice)
But would all this be true even if i chose log function such as the $ log_{10}$. Why do we always turn to the natural logarithm?